Martin Hanzal scored the lone goal for Phoenix.
"It was a great team game," Luongo said. "We're focused on the process."
Higgins opened the scoring 16:29 into the game and Hansen followed with a power-play goal 2:04 later.
Hanzal answered with a power-play goal at 1:34 of the second, but it was all Vancouver after that.
Coyotes goalie Thomas Greiss made 28 saves.
Material from wire services was used in this report.